I loved the first season, but I only liked this season and have a guess that it feels a bit odd for those who haven't read the books. The first season takes place mostly in Lyra's world - similar to our own, but everyone has a "daemon" - a (talking) animal companion, technology is perhaps 50 years behind ours, the world is dominated by the Church, and there's something resembling magic. But some of the first season takes place in our world, mostly in modern Oxford, England. These two sets of events aren't yet noticeably connected. But in the second season the plot lines collide and everything takes place across three worlds, frequently changing between them as characters cross worlds. This was disconcerting for me, someone familiar with the books, and I'm guessing it would be outright disorienting for those less familiar with the storyline.
Dafne Keene, who was so fabulous in the first season as Lyra, mostly looks grumpy and unhappy in this season. The character has some reason to be as she's displaced, pursued, and her and her friend's lives are constantly in peril - but Keene didn't seem up to adding subtlety to Lyra's emotions. But Amir Wilson kind of makes up for it with his performance as Will Parry, a surprisingly kind and decent teenager from our Oxford - despite his messed-up childhood and traveling with Lyra through all of the same difficulties she has.
Lyra is destined / prophesied to do great things (which she cannot be told about or they won't happen). This idea comes from the books, and is carried over to the TV series. One of the things I love about the series is that unlike many children's books, she (and her child companions, notably Will) don't do these great feats alone. They're supported extensively by adults, who often clear the way for Lyra without her ever knowing (and sometimes die for it, and trust me it'll break your heart ...). She still has a massive task ahead of her, but I find it much easier to suspend disbelief than for other children's books where a child (or several) saves the world without any adult assistance.
SPOILER ALERT: I'm going to wreck a semi-important detail of the story, so stop reading etc. I was amused that the adults who have heard from the aliethiometer know - and say in hushed tones - that Lyra is "Eve," and that she's headed for a fall. And yet the church of her world worships "The Authority" (ie. not "God," although the parallels to our Christianity are very clear). This choice of wording goes back to Philip Pullman, and (another spoiler for events probably in season 3) I assume this is because "killing God" would be so much less acceptable than "killing The Authority." We can assure ourselves that this is fiction, and neither Pullman nor the TV series was advocating for killing God. This despite the fact that Pullman has made it clear that he thinks original sin is humanity's greatest strength, and that's kind of the point of the whole series ...